U.S. patent number 6,259,561 [Application Number 09/277,425] was granted by the patent office on 2001-07-10 for optical system for diffusing light.
This patent grant is currently assigned to The University of Rochester. Invention is credited to Nicholas George, Donald J. Schertler.
United States Patent |
6,259,561 |
George , et al. |
July 10, 2001 |
**Please see images for:
( Certificate of Correction ) ** |
Optical system for diffusing light
Abstract
An improved optical system is provided for diffusing light
uniformly over a wide angle, including, a diffractive element for
diffracting light received by the system in multiple diffraction
orders, and a diffusing element which diffuses the diffracted
light. The diffractive element provides diffracted light having an
angular distribution of intensities over the diffraction orders
which is correlated to the power spectrum of the diffusing element
such that the system produces a predetermined intensity
distribution of diffused light. The diffraction period of the
diffractive element is selected such that the angular separation
between the zeroeth and first diffraction orders is approximately
one-half the angular extent of the full-width-at-half-maximum of
the power spectrum of the diffusing element. The strengths of the
diffraction orders are selected such that the combination of
diffused light from each diffractive order provides uniformity in
the intensity of the diffused light from the system.
Inventors: |
George; Nicholas (Pittsford,
NY), Schertler; Donald J. (Rochester, NY) |
Assignee: |
The University of Rochester
(Rochester, NY)
|
Family
ID: |
23060806 |
Appl.
No.: |
09/277,425 |
Filed: |
March 26, 1999 |
Current U.S.
Class: |
359/566; 359/569;
359/591; 359/599 |
Current CPC
Class: |
G02B
5/0221 (20130101); G02B 5/0252 (20130101); G02B
5/0278 (20130101); G02B 5/1814 (20130101); G02B
27/425 (20130101) |
Current International
Class: |
G02B
27/42 (20060101); G02B 5/18 (20060101); G02B
27/44 (20060101); G02B 5/02 (20060101); G02B
005/02 (); G02B 005/18 () |
Field of
Search: |
;359/567,569,574,576,599,591,592,593,594 |
References Cited
[Referenced By]
U.S. Patent Documents
|
|
|
5048925 |
September 1991 |
Gerritsen et al. |
5621487 |
April 1997 |
Shirochi |
5760955 |
June 1998 |
Goldenberg et al. |
5837346 |
November 1998 |
Langille et al. |
|
Other References
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C.N. Kurtz, H.O. Hoadley, and J.J. DePalma, Design and synthesis of
random phase diffusers, Journal of the Optical Society of America,
vol. 63, No. 9, pp. 1080-1092, 1973. .
Nicholas George and Atul Jain, Space and Wavelength Dependence of
Speckle Intensity, Applied Physics, vol. 4, pp. 201-212, 1974.
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on the Space and Wavelength Dependence of Speckle, Applied Physics,
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Karen J. Allardyce and Nicholas George, Diffraction analysis of
rough reflective surfaces, Applied Optics, vol. 26, No. 12, pp.
2364-2375, 1987. .
Lyle G. Shirley and Nicholas George, Diffuser radiation patterns
over a large dynamic range. 1: Strong diffusers, Applied Optics,
vol. 27, No. 9, pp. 1850-1861, 1988. .
Nicholas George, Speckle at various planes in an optical system,
Optical Engineering, vol. 25, No. 6, pp. 754-764, 1986. .
Lyle G. Shirley and Nicholas George, Wide-angle diffuser
transmission functions and far-zone speckle, Journal of the Optical
Society of America A, vol. 4, No. 4, pp. 734-745, 1987. .
E.W. Marchand, Diffraction effects with lenticular projection
screens, Journal of the Optical Society of America, vol. 65, No. 2,
pp. 139-145, 1975. .
Michael D. Kirkpatrick and George Mihalakis, Projection Screens for
High Definition Television, In Large-Screen-Projection, Avionic,
and Helmet-Mounted Displays, SPIE vol. 1456, pp. 40-47, 1991. .
Ralph Bradley, Jr. et al., Ultra-wide viewing angle rear projection
television screen, IEEE Transactions on Consumer Electronics, vol.
CE-31, No. 3, pp. 185-193, 1985. .
Karl M. Jauch & H.P. Baltes, Coherence of radiation scattered
by gratings covered by a diffuser Experimental evidence, Optica
Acta, vol. 28, No. 8, pp. 1013-1015, 1981. .
H.P. Baltes and A.M.J. Huiser, Coherent and incoherent grating
reconstruction, Journal of the Optical Society of America, vol. 3,
No. 8, pp. 1268-1275, 1986. .
D. Newman and J.C. Dainty, Detection of gratings hidden by
diffusers using intensity interferometry, Journal of the Optical
Society of America, vol. 1, No. 4, pp. 403-411, 1984. .
Henry P. Baltes, Speckle correlation and the detection of phase
gratings hidden by diffusers, SPIE vol. 556 International
Conference on Speckle, pp. 223-226, 1985. .
E. Simova and M. Kavehrad, Light Shaping Diffusers for Indoor
Wireless Infrared Communications via a Holographic Approach,
Diffractive and Holographic Optics Technology III, I. Cindrich and
S.H. Lee, ed., SPIE vol. 2689, pp. 284-291, 1996. .
P.C. Clemmow, The Plane Wave Spectrum Representation of
Elecromagnetic Fields, Pergamon Press, New York, pp. 11-38, 1966.
.
M.J. Beesley and J.G. Castledine, The Use of Photoresist as a
Holographic Recording Medium, Applied Optics, vol. 9, No. 12, pp.
2720-2724, 1970. .
R.A. Bartolini, Characteristics of Relief Phase Holograms Recorded
in Photoresists, Applied Optics, vol. 13, No. 1, pp. 129-139, 1974.
.
Stewart Austin and F.T. Stone, Fabrication of thin periodic
structures in photoresist: a model, Applied Optics, vol. 15, No. 4,
pp. 1071-1074, 1976. .
R.C. Enger and S.K. Case, High-frequency holographic transmission
gratings in photoresist, Journal of the Optical Society of America,
vol. 73, No. 9, pp. 1113-1118, 1983. .
Sten Lindau, Controlling the Grove Depth of Holographic Gratings,
Optical System Design, Analysis, and Production, P.J. Rogers and
R.E. Fischer, eds., Proc. SPIE 399, pp. 323-328, 1983. .
Miroslav Miler, Photoresist as a recording material for holographic
elements, SPIE vol. 2108, pp. 2-8, 1993. .
Lyle Gordon Shirley, Laser speckle from thin and cascaded
diffusers, Ph.D. Thesis University of Rochester, The Institute of
Optics, 1988..
|
Primary Examiner: Henry; Jon
Attorney, Agent or Firm: Lukacher; Kenneth J.
Claims
What is claimed is:
1. An optical system for diffusing illumination projected from a
television or a display screen to provide said diffused
illumination uniformly over an angle exceeding 45 degrees in at
least one direction comprising:
a diffractive element for diffracting said projected illumination
to provide diffracted light; and
a diffusing element which diffuses said diffracted light, in which
the diffractive element provides said diffracted light having a
diffraction period, wherein said diffractive element diffracts
light in a plurality of diffraction orders, said diffusing element
has a power spectrum having an angular width, and said diffraction
period of said diffractive element provides an angular separation
between a zeroeth of the diffraction orders and first of the
diffraction orders approximately equal to one-half the angular
width of the power spectrum of said diffusing element.
2. The system according to claim 1 wherein said diffractive element
and said diffusing element are integrated on either side of a sheet
transmissive to said illumination.
3. The system according to claim 1 wherein said diffused
diffractive light has a predetermined intensity of the diffused
illumination at a viewing plane.
4. The system according to claim 1 wherein said diffracted light
represents an intensity distribution of light in accordance with
said diffraction orders, said diffusing element diffuses light from
each of said diffraction orders, and the combination of the
diffused light from each said diffraction order provides a
substantially uniform intensity distribution of diffused light over
said angle.
5. The system according to claim 1 wherein said diffractive element
is a diffraction grating.
6. The system according to claim 1 wherein said diffractive element
represents a diffraction grating profile which is generally
cylindrical.
7. The optical system according to claim 1 wherein said diffractive
element has a structure selected from the group consisting of an
array of circular gratings, an array of elliptical gratings, or a
crossed-grating.
8. An optical system for diffusing light received by the system,
said system comprising:
first means for diffracting the illumination to provide a plurality
of diffraction angular orders; and
second means for diffusing the diffracted illumination at one or
more of the diffraction angular orders in which said first means
has a diffraction period, wherein said second means has a power
spectrum having an angular width, and said diffraction period of
said first means provides an angular separation between a zeroeth
of the diffraction orders and first of the diffraction orders
approximately equal to one-half the angular width of the power
spectrum of said second means.
9. A light diffusing medium for a window, skylight, screen, light
bulb, or light tube comprising:
a first optical surface providing a diffractive element which
diffracts light received by said medium;
a second optical surface providing a diffusing element which
diffuses light diffracted from said first optical layer, in which
said diffractive element has a diffraction period, wherein said
diffractive element diffracts light in a plurality of diffraction
orders, said diffusing element has a power spectrum having an
angular width, and said diffraction period of said diffractive
element provides an angular separation between a zeroeth of the
diffraction orders and first of the diffraction orders
approximately equal to one-half the angular width of the power
spectrum of said diffusing element.
10. An optical system for diffusing light received by the system,
said system comprising:
a first optical element for diffracting light received by the
system in a plurality of diffraction orders; and
a second optical element which diffuses the diffracted light from
said first optical element in accordance with said diffraction
orders to provide diffused light, wherein said second optical
element is a diffuser which has a power spectrum related to the
angle of irradiance of light thereon, said power spectrum having an
angular width, and said first optical element has a diffraction
period which provides an angular separation between a zeroeth of
the diffraction orders and first of the diffraction orders
approximately equal to one-half the angular width of the power
spectrum of the diffuser.
11. An optical system for diffusing light received by the system,
said system comprising:
a first optical element for diffracting light received by the
system; and
a second optical element which diffuses the diffracted light from
said first optical element to provide diffused light, in which said
second optical element has a power spectrum, and said first optical
element has a diffraction period selected in accordance with said
power spectrum of said second optical element, wherein said first
optical element is a diffractive element which diffracts light
received by the system in a plurality of diffraction orders, said
power spectrum of said second optical element has an angular width,
and said diffraction period of said first optical element provides
an angular separation between a zeroeth of the diffraction orders
and first of the diffraction orders approximately equal to one-half
the angular width of the power spectrum of said second optical
element.
12. The system according to claim 11 wherein said system provides a
certain illumination distribution in accordance with the selected
diffraction period of said first optical element and said power
spectrum of said second optical element.
13. The system according to claim 11 wherein the strengths of said
diffraction orders of said first optical element are selected to
obtain uniformity of the intensity distribution of the light from
the second optical element.
14. The system according to claim 11 wherein said diffraction
period represents a periodic phase modulation.
15. The system according to claim 11 wherein said diffracted light
represents an intensity distribution of light in accordance with
said diffraction orders, said second optical element diffuses light
from each said diffraction order, and the combination of the
diffused light from each said diffraction order provides a
predetermined intensity distribution of said diffracted light from
said second optical element.
16. The system according to claim 15 wherein the diffused light
from each of said diffraction orders contribute to said
predetermined intensity distribution to provide a substantially
uniform intensity distribution of diffused light over an angular
range.
17. The system according to claim 15 wherein said intensity
distribution of the diffracted light in the far field is a
superposition of the individual intensity distributions from the
second optical element when illuminated with said angular intensity
distribution weighted by the strengths of the diffracted light for
each of the diffraction orders.
18. The system according to claim 11 wherein said diffused light
from said second optical element has a substantially uniform
intensity distribution over a wide angle greater than 45
degrees.
19. The system according to claim 18 wherein said wide angle is
approximately 90 degrees.
20. The system according to claim 11 wherein said diffractive
element of said first optical element faces said second optical
element.
21. The system according to claim 11 wherein said diffractive
element of said first optical element faces away from said second
optical element.
22. The system according to claim 11 wherein said first optical
element and said second optical element are spaced a distance from
each other.
23. The system according to claim 11 wherein said first optical
element and said second optical element are integrated on a single
body.
24. The system according to claim 11 wherein said first optical
element has a surface providing a diffraction grating, and said
second optical element has a surface to diffuse light received from
said first optical element.
25. The system according to claim 11 wherein said first optical
element is a diffraction grating.
26. The system according to claim 25 wherein said diffraction
grating represents one of a holographic diffraction grating and a
surface relief diffraction grating.
27. The system according to claim 25 wherein said diffraction
grating having one of a cylindrical structure and a circular
symmetric structure.
28. The system according to claim 25 wherein said grating is one of
a one-dimensional and two-dimensional grating.
29. The system according to claim 25 wherein said grating has a
structure representing one of a crossed grating and a circular
grating.
30. The system according to claim 25 wherein said grating has a
structure representing an array of circular gratings.
31. The system according to claim 25 wherein said grating has a
structure representing an array of elliptical gratings.
32. The system according to claim 11 wherein said second optical
element is a parabolic diffuser.
33. The system according to claim 11 wherein said second optical
element is substantially thinner with respect to said first optical
element.
34. The system according to claim 11 wherein said second optical
element has a small angle scattering pattern.
35. The system according to claim 11 wherein said first and second
optical elements are part of a window.
36. The system according to claim 11 wherein said first and second
optical elements are part of a skylight.
37. The system according to claim 11 wherein said first and second
optical elements represent an envelope of a light bulb or tube.
38. The system according to claim 11 wherein said first and second
optical elements are part of a projection television.
39. The system according to claim 11 wherein said first and second
optical elements are part of a display screen.
40. The system according to claim 11 wherein said first optical
element represents a plurality of optical elements, and said
diffractive element represents a plurality of diffractive elements
on said plurality of optical elements, in which said plurality of
diffractive elements provides said plurality of diffraction
orders.
41. The system according to claim 11 further comprising at least
one light source for providing light to said first optical
element.
42. The system according to claim 41 wherein said light from said
light source has a plurality of wavelengths.
43. The system according to claim 41 wherein said light from said
light source is monochromatic.
44. The system according to claim 41 wherein said light provided to
said first optical element is received through said second optical
element and reflected and diffracted by said first optical element
to said second optical element.
45. The optical system according to claim 11 wherein said first
optical element has first and second sides in which said second
side faces said second optical element, and said optical system
further comprising an image transparency adjacent said first side
of the first optical element.
46. A method for diffusing light from one or more light sources for
improving illumination of an area comprising the steps of:
diffracting the light to provide a plurality of diffraction angular
orders having an angular separation;
diffusing the diffracted light in accordance with a power spectrum
of diffusion at one or more of the diffraction angular orders in
which said angular separation is selected in accordance with the
power spectrum; and
illuminating an area with said diffused light, wherein said angular
separation between a zeroeth of the diffraction angular orders and
first of the diffraction angular orders is approximately equal to
one-half the angular width of the power spectrum.
47. The method according to claim 46 wherein the strengths of said
diffraction angular orders are selected to obtain uniformity of the
intensity distribution of said diffused light.
48. The method according to claim 46 wherein said diffracted light
represents an intensity distribution of light in accordance with
said diffraction angular orders, said diffusing step diffuses light
from each said diffraction order, and the combination of the
diffused light from each said diffraction order provides a
predetermined intensity distribution of said diffracted light.
49. The method according to claim 48 wherein the diffused light
from each of said diffraction angular orders contribute to said
predetermined intensity distribution to provide a substantially
uniform intensity distribution of diffused light over an angular
range.
50. The method according to claim 46 wherein said diffused light
has a substantially uniform intensity distribution over a wide
angle greater than 45 degrees.
51. The method according to claim 46 wherein said diffusing step
diffuses light with a small angle scattering pattern.
52. The method according to claim 46 further comprising the step of
providing at least one light source for light to said diffracting
step.
53. The method according to claim 52 wherein said light source is
sunlight.
54. The system according to claim 25 wherein said grating is a
one-dimensional grating.
55. The system according to claim 41 wherein said light from said
light source is first incident said first optical element of the
group of said first and second optical elements.
56. The system according to claim 41 wherein said light from said
light source is sunlight.
57. An optical system for diffusing light comprising:
a first optical element for diffracting light, and a second optical
element for diffusing light having a parabolic surface correlation,
in which said first and second optical elements are in a cascade
relationship providing an intensity distribution I.sub.p from light
received by the system in accordance with ##EQU32##
wherein .theta. and .phi. are the scattering angles of the light
received by the system, .lambda. is the wavelength of light,
l.sub.c is the surface correlation length of the second optical
element, and S is the rms phase delay of the second optical element
in accordance with ##EQU33##
wherein .sigma. is the rms surface height, .LAMBDA. is the grating
period of the first optical element based upon the
full-width-at-half-maximum of the power spectrum of the second
optical element, n is the refractive index of the second optical
element, and variable j represents a diffraction order of the first
optical element, B.sub.j.sup.2 are the strength values of the
diffraction orders of the first optical element, in which said
strength values are optimized to obtain a power spectrum of the
light from the system which is substantially uniform over an
angular range.
58. The optical system according to claim 57 wherein the angle of
the first diffraction order of the first optical element is near
the angle at which the power spectrum of the second optical element
is approximately one half the peak value of the power spectrum, and
said diffraction period is in accordance with the angle of first
diffraction order.
59. The optical system according to claim 57 wherein said
full-width-at-half-maximum of the power spectrum of the second
optical element is in accordance with l.sub.c /.lambda.S.
Description
DESCRIPTION
1. Field of the Invention
The present invention relates to an optical system (and method) for
diffusing light, and relates particularly to, an optical system
having a diffractive element and a diffusing element, which
diffuses light diffracted from the diffractive element. The
invention is especially suitable for diffusing light for a
projection television (TV) or display screen, or diffusing light
for a window, skylight, light bulb or light tube, such that the
diffused light has a uniform intensity distribution over a wide
angle.
2. Background of the Invention
Optics for diffusing light is typically used for large screen
projection TV's, and includes a lenticular array consisting of
vertically oriented cylindrical lenslets formed in a plastic sheet.
The array distributes the light horizontally by an angular amount
determined by the numerical aperture of the individual lenslets.
Typical commercially available screens with a lenticular array have
poor efficiency, 30% or less, and have undesirable color banding
and white and dark lines at the edges of the pattern due to the
diffraction effect of the lenslet array. Often a two-sided
lenticular screen is used for projection TV's having a black
absorbing stripe between lenslets to increase the screen contrast
and reduce ambient room-light reflections. One proposed design
described in R. J. Bradley, J. F. Goldenberg and T. S. McKechnie,
"Ultra-wide viewing angle rear projection television screen," IEEE
Trans., Consum. or Electronics. CE-31, p.185-193 (1985),
incorporates a complex lenticular surface, a bulk diffuser and
black striping. The screen is reported to have a nearly uniform
luminance pattern over a .+-.90.degree. range giving rise to an
intensity distribution that falls off as a cosine of the scattering
angle. The bulk diffuser is used to spread the light vertically. In
this design, like in the typical projection TV, the diffusing
optics does not use diffraction in multiple diffraction orders to
enhance the diffusing of light.
Diffusing of light is also used for skylights. Typically, the
skylights have a clear window pane installed at roof level of a
room followed by a deep well that is painted white. The deep well
acts as a diffusing reflector to prevent direct sunlight from
reaching the room. Often when large skylights are used, special
shaped diffusing reflectors are installed, such as in the Musee
d'Orsay in Paris, France. While diffusing reflectors are effective,
they are expensive and unaesthetic. Accordingly, it would be
desirable to diffuse light from a skylight without the need for a
diffusing reflector.
Diffusing of light may also be provided by frosting of glass used
for windows, or in the area of artificial light, by the frosting of
light bulbs. However, such light diffused through frosted glass is
often not as uniform as desired.
The present invention relates to an optical system for diffusing
light for use in illumination or display applications having a
cascade of a diffractive element, such as a grating, and a thin
diffusing element, referred to as a diffuser. Although cascades of
a grating and a diffuser have been proposed in other areas, they
have been limited to the analysis of coherence properties, such as
discussed in K. M. Jauch and H. P. Baltes, "Coherence of radiation
scattered by gratings covered by a diffuser. Experimental
evidence," Optica Acta 28, 1013-1015 (1981), detecting gratings
hidden by diffusers, such as discussed in D. Newman and J. C.
Dainty, "Detection of gratings hidden by diffusers using intensity
interferometry," J.Opt.Soc.Am. A 1, p. 403-411 (1984), or for use
with wireless communication systems, such as discussed in E. Simova
and M. Kavehrad, "Light shaping diffusers for indoor wireless
infrared communications via a holographic approach," in Diffractive
and Holographic Optics Technology III, I. Cindrich and S. H. Lee,
ed., Proc. SPIE 2689, 284-291 (1996). The prior art cascades of a
grating and a diffuser do not produce over a wide angle the uniform
diffused light needed for illumination and display
applications.
SUMMARY OF THE INVENTION
It is the principal object of the present invention to provide an
improved optical system for diffusing light uniformly over a wide
angle.
Another object of the present invention is to provide an improved
optical system for diffusing light for projection TV's with greater
efficiency than the prior art lenticular screens, and can easily
replace such lenticular screens.
A further object of the present invention is to provide an improved
optical system for diffusing light which can be used as, or in
combination with, windows or skylights, without requiring diffusing
reflectors.
Yet a further object of the present invention is to provide an
improved optical system for diffusing light produced by a display
screen.
Another object of the present invention is to provide an improved
optical system for diffusing light which utilizes a diffractive
element for providing multiple diffraction orders.
A still further object of the present invention is to provide an
improved optical system for diffusing light which can be placed on
two sides of a single sheet of light transmissive material.
Briefly described, the optical system embodying the present
invention includes a diffractive element for diffracting light
received by the system in multiple diffraction orders, and a
diffusing element which diffuses the diffracted light from the
first optical element in accordance with the diffraction orders to
provide diffused light.
The diffractive element provides diffracted light to the diffusing
element having an intensity distribution in the form of a number of
individual beams, termed diffraction orders, that are spaced by an
angular separation determined by the diffraction period of the
diffractive element and the illuminating wavelength or wavelengths.
The intensity distribution of the diffracted light is correlated
with the angular dependent intensity of scattered light provided by
the diffusing element, which may be called the power spectrum of
diffusion, such that the combination of the diffused light from
each diffraction order provides a substantially uniform intensity
over an observation zone or plane.
The correlation of the intensity distribution of the diffracted
light to the diffusing element is such that the angular separation
between the zeroeth diffraction order and the first diffraction
order is approximately equal to one-half the angular width of the
power spectrum of the diffusing element. The angular width
represents the full-width-at-half-maximum of the power spectrum of
the diffusing element. The strengths (intensity) of the diffraction
orders are selected such that the combination (sum) of the diffused
light from each diffraction order provides uniformity in the
intensity of the diffused light from the system in the far field.
Thus, the intensity distribution of the diffused light in the far
field represents a superposition of the individual intensity
distributions from the diffusing element when illuminated at the
angle provided by each diffraction order of the diffracted light
weighted by the strengths of the diffraction orders. The weights of
the strength of the diffraction orders are such that the diffused
light from each diffraction order contributes to provide a uniform
combined intensity distribution of diffused light over a wide
angle, such as between 45 and 100 degrees.
The diffractive element may represent a diffraction grating. The
structure of the diffraction grating may be one-dimensional or
two-dimensional. The diffusing element may have a surface which
provides scattering at small angles (less than 10 degrees) of light
incident on the diffusing element. The diffractive and diffusing
elements may either be spaced a distance from each other, or
integrated on a single body, such as on the two sides of a sheet of
light transmissive material.
The combination of diffusing and diffractive elements can provide
diffused light having a uniform intensity distribution over a wide
angle in one direction with a much smaller angle in the other,
which is desirable for a projection TV or the like. The combination
of diffusing and diffractive elements can also provide diffused
soft-light, such as for window or skylight, by selection of an
appropriate grating structure for the diffractive element. The
present invention is also applicable to other illuminating or
display applications to provide high efficiency diffusing of light,
such as display screens, microfilm viewers, greenhouses,
illuminating signs, billboards, light bulbs and light tubes.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing objects, features and advantages of the invention
will become more apparent from a reading of the following
description in connection with the accompanying drawings in
which.
FIGS. 1A and 1B are optical diagrams of the system according to the
present invention having a diffractive element (in the form of a
diffraction grating on the surface thereof) and a diffusing element
(referred to as a diffuser), in which FIG. 1A shows the diffraction
grating oriented to face the diffuser, and FIG. 1B shows the
diffraction grating oriented to face the illumination;
FIG. 1C is an optical diagram of the system according to the
present invention in which the diffraction grating and diffuser are
part of a single body;
FIG. 2 is a optical diagram showing the scattering angles for a
typical diffuser;
FIG. 3 is a graph illustrating the total scattered power from a
parabolic and conical surface correlation functions for a
mathematical model of the diffuser of FIG. 2 as a function of rms
phase delay S for fixed correlation length;
FIG. 4A is a graph illustrating the scattering patterns (relative
intensity at varying scattering angles) for a parabolic diffuser
for l.sub.c /(.lambda.S)=1 at five illumination angles of
0.degree., .+-.20.degree., and .+-.43.20.degree. and the sum of
their scattering patterns;
FIG. 4B is a graph illustrating the scattering patterns for a
parabolic diffuser of FIG. 4A scaled by the normalized coefficients
of Table I, and the optimized sum of the resulting scattering
pattern of the combination of the diffraction grating and the
diffuser of the system shown in FIG. 1A;
FIG. 5A is a graph illustrating the scattering patterns for a
parabolic diffuser for l.sub.c /(.lambda.S)=4 at illumination
angles corresponding to the diffraction angles of a 5.degree.
grating, and the sum of their scattering patterns;
FIG. 5B is a graph illustrating the scaled scattering patterns for
a parabolic diffuser of FIG. 5A, and the optimized sum of the
resulting scattering pattern of the combination of the diffraction
grating and the diffuser of the system shown in FIG. 1A;
FIG. 6 is a graph illustrating the wavelength variation of the
scattering pattern of the optimized sum of FIG. 5B for the
combination of the diffraction grating and the diffuser;
FIG. 7 is a scanning electron micrograph of a 5.degree. grating
suitable for the diffraction grating used in an example of the
system of FIG. 1A;
FIG. 8 is a graph illustrating the scattering pattern of the
diffuser for single beam illumination in ample of the system of
FIG. 1A;
FIG. 9 is a graph illustrating the scattering pattern of the
diffused light in the example of the system of FIG. 1A for multiple
wavelengths with a 5.degree. diffraction grating and a diffuser, as
measured in the plane of the grating diffraction orders;
FIG. 10 is a graph illustrating the scattering pattern for a
commercially available microfiche view screen;
FIG. 11A is an optical diagram of another embodiment of the system
of the present invention having two diffraction gratings and a
diffuser;
FIG. 11B is a graph illustrating the scattering pattern of the
diffused light in multiple wavelengths in an example of the system
of FIG. 11A having a 5.degree. grating, a 15.degree. grating, and a
diffuser, as measured in the plane of the grating diffraction
orders;
FIG. 12 is a graph illustrating the full-width-at-half-maximum
versus rms phase delay, S, of the power spectrum for the parabolic
and conical surface correlation functions of a diffuser for l.sub.c
/.lambda.=10, in which the efficiencies at different lobe widths
are denoted by the percentages;
FIG. 13 is a graph illustrating the small angle scattering patterns
from a diffuser in the system of the present invention, 3M Magic
Tape type 810, frosted microscope slide, and glass etched with
Armour Etch, in which the efficiency of each is denoted by the
percentages;
FIG. 14A is an optical diagram of the system according to the
present invention having two diffractive elements, in the form of
crossed gratings, and a diffusing element;
FIG. 14B is an optical diagram of the system according to the
present invention having a diffractive element and a diffusing
element in which the diffractive element is a circular grating;
FIG. 15A is a graph illustrating the scattering pattern of the
diffused light in an example of the system of FIG. 14A showing a
circular symmetric pattern over a 90.degree. span;
FIG. 15B is a graph illustrating the scattering pattern of the
diffused light in an example of the system of FIG. 14A showing an
asymmetric pattern with a 90.degree. span in the horizontal
direction and a 30.degree. in the vertical direction;
FIG. 15C is a graph illustrating the scattering pattern of the
diffused light in an example of the system of FIG. 14B showing a
circular symmetric pattern over a 90.degree. span;
FIG. 16A is an optical diagram of the system according to the
present invention having a diffractive element d a diffusing
element in which the diffractive element is an array of circular
gratings with the circular gratings arranged side by side;
FIG. 16B is an optical diagram of the system according to the
present invention having a diffractive element and diffusing
element in which the diffractive element is an array of overlapping
circular gratings; and
FIG. 17 is an example of the system of the present invention in
which either an image transparency, or picture or print with a
reflective surface, lies adjacent the diffractive element of the
system.
DETAILED DESCRIPTION OF THE INVENTION
Referring to FIGS. 1A and 1B, the optical system 10 for diffusing
light 12 is shown. System 10 includes a first optical element 14
for diffracting light and a second optical element 18 for diffusing
light. The diffractive element 14 may represent a periodic
diffraction grating. The diffusing element 18 has a rough surface
20 providing a narrow scattering angle for the diffusing of light.
The diffusing element 18 is illuminated at multiple angles
simultaneously by the diffracted light 17 from the diffractive
element 14, such that the combination of the intensity patterns of
scattered light produced by the diffusing element at each
diffraction order of the diffracted light provides a substantially
uniform intensity of diffused light 22. The intensity distribution
of the diffused light 22 in the far field is a superposition of the
individual intensity patterns weighted by the strengths of the
diffraction orders. The combination of the diffractive element 14
and diffusing element 18 is referred to herein as a cascade.
In FIG. 1A, the diffractive element 14 is oriented such that the
surface 16 of the diffractive element, which presents a grating,
faces the diffusing element 18. In FIG. 1B, system 10 is shown in
which the diffractive element 14 is oriented such that the surface
16 faces the light 12 received by the system. Depending on the
application of the optical system 10, the source of light 12 may be
sunlight, illumination from a screen of a display or projection
television, an artificial light source, or any other light where
diffusion (or scattering) is desired. For purposes of illustration,
the source of light 12 is shown as block 11, which maybe part of
system 10 or separate from the system.
Diffractive and diffusing elements 14 and 18 may be on separate
bodies as shown in FIGS. 1A and 1B, or the system 10 may be
integrated on a single body 24, as shown in FIG. 1C. Body 24 may
represent a medium such as a sheet of plastic, glass or metal in
which one surface 24a provides the diffractive element 14 and the
other surface 24b provides the diffusing element 18. Such a sheet
can readily replace the lenticular array screen commonly used in
projection televisions, or be used as, or in combination with, a
window or skylight. The profile structure of the grating of the
diffractive element may be linear or cylindrical, or circular
symmetric, depending on the desired spatial distribution of the
diffused light.
The system 10 produces diffused light which is scattered
substantially uniformly in an angular range selected by the
characteristics of the diffraction period and the angular orders of
diffraction of the diffractive element 14, and the scattering
properties of the diffusing element 18, for the wavelength or
wavelengths of light to be diffused, as described later below. When
the grating structure of the diffractive element is linear or
cylindrical, similar to lenticular optics, the scattering pattern
produced by the system can be spread fan-like over a wide angle in
one-plane, such as between 65 and 100 degrees, and a smaller range
in the other plane, such as between 15 and 50 degrees. The diffused
light from the system may be substantially uniform within this
angular range, such as within .+-.1 db. The system 10 can diffuse
single or multiple wavelengths of light, and can have an optical
efficiency of up to 95% depending on the wavelength(s) and the
optical characteristics of the diffractive and diffusing elements
14 and 18.
In system 10 of FIGS. 1A-1C, the grating structure shown for
diffractive element 14 is one-dimensional such that the
illumination from the system is substantially uniform over a wide
angle in one-dimension. A circularly symmetric or other
two-dimensionally tailored uniform illumination can also be
produced using a diffractive element 14 having a two-dimensional
grating structure as shown in the system 10a of FIGS. 14A and 14B.
System 10a is similar to system 10, but incorporates an element 14
with a two-dimensional grating structure. The two-dimensional
structure, for example, may be a crossed grating structure, as
shown in FIG. 14A, or a circular grating structure, as shown in
FIG. 14B. The crossed grating diffractive element of FIG. 14A has
corrugations that run perpendicular to one another to produce
diffracted light 25 having diffraction orders in a two-dimensional
array. The angular spread of these orders is determined by the
respective grating period of the diffractive element in each
dimension. The crossed grating structure may be formed on either
side 16a and 16b of a single diffractive element, or it may be
formed on one side of a single element, or it may be formed by
combining two single-sided diffractive elements. If the crossed
grating structure is formed by two elements then the corrugations
may be positioned in one of several configurations: both elements
having the corrugations facing the illumination 12, both facing the
diffusing element 18, or one facing the illumination and the other
facing the diffusing element. In any configuration, the
corrugations are oriented perpendicular to one another. The
two-dimensional array of diffractive orders of the diffracted light
25 is received by the diffusing element 18 to provide a
two-dimensional soft-diffused uniform illumination. By controlling
the strengths of the diffraction orders in diffracted light 25, a
circular symmetric illumination can be provided from the system, as
illustrated in FIG. 15A. By changing the strengths of the orders in
one dimension, a tailored illumination can be produced from the
system that is uniform, for example, over 90.degree. horizontally
and 30.degree. vertically, as illustrated in FIG. 15B. The system
10a with a cross-grating diffractive element can be useful as a
projection screen, such as for a projection television, due to the
regularity of the grating structure.
A circular grating used as the diffractive element 14 in FIG. 14B
directs normally incident light into many concentric cones of
diffracted light 27. The angular spread of the cones is determined
by the grating period of the diffractive element 14. The depth of
the grating structure determines the amount of light diffracted
into each cone. Each cone is received by the diffusing element 18
to provide a circular symmetric soft-diffused illumination from the
system. These systems can be useful in providing a soft-light
diffuser which can be used as, or in combination with, a window or
skylight.
Further, the diffractive element 14 may have an array of circular
gratings 16c, as shown in system 10b of FIGS. 16A and 16B. System
10b is similar to system 10 and 10a, but incorporates a circular
grating array. These gratings may be nested side by side with their
edges touching, as shown in FIG. 16A, or the diffractive element
may be constructed with overlapping circular gratings, as shown in
FIG. 16B. For example, in FIG. 16B the center-to-center spacing of
each circular grating may be one-half the grating diameter. System
10b is useful for projection screen or billboard applications, or
the like, in which a picture or image is placed against or
projected onto the optical system of the invention. Projection
involves directing image illumination 12, which may represent an
array of pixels in one or more color channels, to the diffractive
element 14. In certain other display applications, an image
transparency may be placed adjacent (against or near) the
diffractive element 14, such that light representing the image from
the transparency passes to the diffractive element 14 when light is
received by the system. For example, FIG. 17 shows an image
transparency 28 adjacent one side of diffractive element 14, where
the other side of the diffractive element 14 faces diffusing
element 18, in which light 12 is received by system 10b through the
transparency. In further display applications, the cascade of the
diffractive element 14 and diffusing element 18 may provide, or be
a part of, a cover or screen for media having a reflective surface,
for example, a print or picture, which is illuminated by reflected
light that passes through the cascade to the media. This is also
shown in the example of FIG. 17 in which 28 represents a print or
picture lying adjacent the diffracting element 14, such that light
12a, rather than light 12, received through optical elements 14 and
18 is reflected from the surface of the print or picture through
optical elements 14 and 18 to provide diffused reflected light from
element 18 to each person viewing the print or picture.
In system 10b, each of the circular gratings or sites 16c (FIGS.
16A and 16B) may be associated with a small cluster of pixels
having one or more pixels, such as 8.times.8 pixels, from an image
placed against or projected onto the diffractive element 14. Thus,
light from each pixel cluster is diffracted and diffused as it
passes through its circular grating 16c and then the diffusing
element 18 to spread uniformly to a viewing audience. System 10b
produces a circular symmetric intensity distribution. Elliptical
gratings, i.e., gratings with a larger grating period in one
dimension than the other, may be used rather than circular gratings
to tailor the intensity distribution from system 10b to particular
viewing angles. Such a diffractive element 14 having an array of
elliptical gratings can produce concentric elliptical cones of
illumination to the diffusing element 18, and thus provide a large
horizontal uniform distribution and a narrower vertical uniform
distribution of light from system 10b.
The cascade of diffractive element 14 and diffusing element 18 can
also be used as an envelope for a light bulb or light tube where
controlled illumination is required, such as for sign or billboard
illumination, street lights, store displays, and the like.
Elements 14 and 18, or body 24, may be made of glass, plastic,
ceramic, or semiconductor, or other light transmissive to the
illumination to be diffused. The diffractive element 14 may have an
etched, embossed, or holographically recorded grating, depending on
the type of material used, and diffusing element 18 may be
similarly produced to create the desired rough surface. In
particular, using plastics, such as polyethylene-or polycarbonate,
the profile structure of the diffusing element 18 and a diffractive
element 14 can be embossed, molded, or stamped using typical
manufacturing methods. For example, optical elements 14 and 18 can
be made of polyethylene or polycarbonate.
The system can also be configured for use in reflection by placing
the thin diffusing element 18 directly in front of a reflective
diffractive element 14. The system in a reflective configuration is
similar to the cascades shown in FIGS. 1A-1C, 14A-14B, and 16A-16B,
except that incident light 12 received by the system passes through
diffusing element 18 to a reflective, diffractive surface 16 of
diffractive element 14, and then the diffracted light produced by
element 14 passes through the diffusing element 18 to provide
diffused light. This configuration can be used for front projection
screens.
The diffused light provided by system 10 is substantially uniform
over a wide angle as shown by the below theory which first
describes a mathematical model of a diffusing element and then
field equations defining the combination of the diffracting element
14 and the diffusing element 18. The diffracting element 14 is
referred to herein as a grating, and the diffusing element 18 is
referred to herein as a diffuser.
Referring to FIG. 2, the scattering from a diffuser 26 is shown
having roughness h(x', y') in which (x', y') are transverse
coordinates in the plane of the diffuser. For diffuser 26 located
in the plane z=0 and illuminated by a linearly polarized
monochromatic plan wave, the scalar component of the far zone
electric field is ##EQU1##
where the integral is limited to a finite aperture. The point of
observation, (x, y, z), is a distance R.sub.0 from the origin and k
is the wave number 2.pi./.lambda. for a wavelength .lambda.. A
harmonic time dependence of exp(i.omega.t) is implicitly used.
The term .nu..sub.II is the scalar component of the field emerging
from the object in the plane z=0. It depends on the incident
illumination and the transmission function of the diffuser. The
field incident on the diffuser is decomposed into an angular
spectrum of plane waves. If .nu. is the analytic signal
representation of the temporal Fourier transform of the time
varying real-valued electric field, then the angular spectrum, V,
in a plane parallel to the xy plane is defined by the two
dimensional spatial Fourier transform relation
with the corresponding inverse given by
This is discussed, for example, in P. C. Clemmow, The Plane Wave
Spectrum Representation of Electromagnetic Fields (Pergamon Press,
New York, 1966). The variable .nu. is the temporal frequency.
The relationship between the spatial frequencies f.sub.x and
f.sub.y and the direction cosines .alpha. and .beta. with respect
to the x and y axes is ##EQU2##
The transmission function, t(x',y';.alpha.,.beta.), of an object is
that function which, when multiplied by a given input plane waves
produces the output field .nu..sub.II. From Equation (3) the
differential field d.nu. that emerges from a transmission object
illuminated by a plane wave of frequencies f.sub.x and f.sub.y and
strength V.sub.I is given by the incident plan wave times the
transmission function of the object for that plane wave, i.e.,
where the transmission function is written with the spatial
frequencies. The total field is then the integral over all spatial
frequencies incident on the object. Equation (5) represents the
general case of transmission functions. If the object is
independent of the input direction cosines, as in the case of a
simple aperture, for example, then integration of Equation (5)
yields an output field that is the product of the total input field
and the transmission function.
For the special case of discrete incident plane waves, V.sub.I can
be written in the plane z=0 as ##EQU3##
where each plan wave has an amplitude B.sub.j and direction cosines
.alpha..sub.j and .beta..sub.j.
From this, the field .nu..sub.II exiting the diffuser is
determined, ##EQU4##
where t.sub.D (x',y ',.alpha..sub.j,.beta..sub.j) is the
transmission function of the diffuser for the input direction
cosines .alpha..sub.j and .beta..sub.j. Further analysis of the
diffuser will be done for a single incident monochromatic
unit-amplitude plane wave.
The transmission function, t.sub.D, for a thin diffuser is given
by
where n is the index of refraction and .theta..sub.1 is the
refraction angle in the diffuser medium. The angle .theta..sub.2 is
the output angle which depends on .theta..sub.1, n, and the local
surface slope by means of Snell's law, and h(x', y') is the
zero-mean surface height profile measured in the +z direction. The
constant phase term due to the average thickness, H, of the
diffuser substrate can be dropped. If it is assumed that the
surface slopes are small then the output angle, .theta..sub.2, can
be replaced by the input angle, .theta..sub.0. Equation (8) is
described, for example, in N. George, "Speckle at various planes in
an optical system," Opt. Eng. 25, p.754-764 (1996), and L. G.
Shirley and N. George, "Wide angle diffuser transmission functions
and far zone speckle," J.Opt.Soc.Am A 4, p.734-745 (1987).
Next, the envelope or average intensity pattern that results from
an ensemble of statistically identical diffusers is determined. The
ensemble average of the intensity is ##EQU5##
It is normalized by the total incident power on the diffuser, which
is proportional to the aperture area, A, and is multiplied by the
square of the distance R.sub.0. The result is a function of the
scattering angles .theta. and .phi., and has units of
1/steradian.
The resulting intensity for a Gaussian surface height distribution
is given in L. G. Shirley and N. George, "Diffuser radiation
patterns over a large dynamic range. 1: Strong diffusers," Appl.
Opt. 27, p. 1850-1861 (1988), as ##EQU6##
where the integral is over the illuminating aperture and the cos
.theta. is to the first power. J.sub.0 is the zero-order Bessel
function. The rms phase delay S for a given illumination angle
.theta..sub.0 is ##EQU7##
where, as described in the above-cited paper by L. G. Shirley and
N. George, .sigma. is the rms height of the diffuser.
The surface correlation function, r.sub.12, characterizes the
structure of the surface. It is approximated by one of the
following two forms obtained from the first two terms in a series
expansion and represents extremes in surface structure. A surface
with slowly varying and continuous slopes can be represented by a
parabolic correlation function given by ##EQU8##
where l.sub.c is the correlation length. A surface with a conical
correlation has steep, discontinuous slopes and can be approximated
by ##EQU9##
The resulting forms for the expected intensity using these two
representations are ##EQU10##
for the parabolic surface denoted by the subscript P and
##EQU11##
for the conical surface denoted by the subscript C. These forms are
derived from Equations (36) and (34), respectively, as described in
the earlier cited paper by L. G. Shirley and N. George.
For the purposes of a display, a diffuser with a broad scattering
envelope and a high power throughput is desired. For the cases
above the angular width of the scattering envelope increases as the
roughness, either .lambda.S/l.sub.c or .lambda.S.sup.2 /l.sub.c,
increases. The total power scattered into the +z hemisphere, as
determined from Equations (14) and (15) by integrating over .theta.
and .phi., decreases with increasing roughness. This is shown in
the graph of FIG. 3 of the normalized total scattered power versus
S for a fixed correlation length. Thus, there is a trade off
between lobe width and power throughput. However, the total power
from the parabolic surface is larger than the conical surface for a
given rms phase delay, S, and correlation length, so this type of
surface will be considered. The properties of these equations are
analyzed as follows:
Of the scattering properties of Equations (14) and (15) relative to
the scattering angles for diffusers, the most important herein are
the efficiency and lobe width. The lobe width, which is also
referred to as the fill-width-at-half-maximum, is determined from
the power spectrum of the diffuser 18, i.e., the intensity pattern
of scattered light from the diffuser as a function of scattering
angle. As the roughness increases for both the parabolic and
conical surface correlations the lobe width increases but the
efficiency decreases. This is shown graphically in FIG. 12 in which
the full lobe width in degrees is plotted versus the rms phase
delay for a fixed correlation length. Each surface type is shown
with the efficiency taken from FIG. 3 shown as a percentage. The
tradeoff in efficiency with lobe width is most severe for the
conical surface showing a 10% loss at only 10.degree. lobe width.
The parabolic diffuser, however, can provide a 50.degree. lobe
width with less than 5% reduction in efficiency.
The scattering patterns of several materials are shown in FIG. 13
including the diffuser used for the cascade, a diffuser etched for
30 minutes in Armour Etch, 3M Magic Brand Tape (type 810), and a
frosted microscope slide. The efficiency is given by the percentage
next to each name. The 3M tape makes an excellent diffuser with the
same efficiency as the cascade diffuser, however, the cascade
diffuser is better suited to the issue at hand since it scatters
mostly in the central lobe. The frosted glass and Armour etched
diffuser are significantly less efficient yet have a similar lobe
width. Thus, they are less desirable for use as a projection
screen.
The intensity distribution from the parabolic diffuser, unlike the
conical diffuser, is independent of wavelength aside from the
variation in the index of refraction, n, in the rms phase delay,
S.
The above description discussed the expected intensity pattern of a
model diffuser 26 (FIG. 2) illuminated by a plane wave at an
arbitrary incident angle. Using this model diffuser, system 10
having a diffuser and grating will now be mathematically
described.
Referring back to FIG. 1, to broaden the diffuser pattern while
maintaining high throughput efficiency, optical system 10 is
provided in which a narrow-scattering-angle diffuser 18 is
illuminated simultaneously at multiple incident angles by a
diffraction grating 14 placed in front of the diffuser. As stated
earlier, the resulting intensity distribution from diffuser 18 is a
superposition of the individual intensity patterns weighted by the
strengths of the grating diffraction orders. To show this, the
field exiting the combination of the grating 14 and diffuser 18 is
described mathematically below.
The grating is illuminated by a monochromatic normally-incident
plane wave of unit amplitude followed by a diffuser in one of the
configurations shown in FIGS. 1A-1C. In any case, the incident
spectrum at the grating V.sub.I is a delta function
.delta.(f.sub.x, f.sub.y) and the field exiting the grating, from
Equation (5) is simply the transmission function of the grating
given by the general form ##EQU12##
where f is the grating period and B.sub.j are the amplitudes of the
diffraction orders. This field is then decomposed into its angular
spectrum which is given as the 2-D Fourier transform of the grating
transmission function. The transform is ##EQU13##
where .Fourier. represents the 2-D Fourier transform and the
frequency-variable arguments of the delta functions give the
angular direction of the diffraction orders. The first delta
function restricts the k vectors of the diffracted plane waves to
the xz plane, i.e., .phi.=0 or .pi.. The second delta function is
non-zero when f.sub.x is an integer divided by the grating period,
.LAMBDA.. From Equation (4) sin .theta.=x/R.sub.0 =-.lambda..sub.0
f.sub.x which gives the familiar grating equation sin
.theta.=m.lambda..sub.0 /.LAMBDA., for an integer m. The summation
has fixed limits to maintain a physically realizable diffraction
angle.
This discrete spectrum of plane waves illuminates the diffuser as
in Equation (6). For each plane wave exiting the grating the
appropriate diffuser transmission function is written given in
Equation (8) including the phase delays due to the separation of
the planes of the grating and diffuser. If V.sub.II represents the
angular spectrum of the field exiting the grating at plane II, then
the field exiting the diffuser is
where z is set to zero (z=0) since the grating is taken to be at
this plane. Inserting the angular spectrum of the grating and the
diffuser transmission function, the result for the forward grating
of FIG. 1A is obtained,
##EQU14##
The subscript j on the angle .theta. indicates the incident angle
to the diffuser. Similar expressions result for the configurations
of FIGS. 1B and 1C, but with different phase terms due to the
separations of the surfaces. The relationship between the spatial
frequency variables and the incident angles is ##EQU15##
Performing the integration yields ##EQU16##
This is the field exiting the cascade. The angular relationships
are ##EQU17##
The far zone expression for the field from Equation (1) then
becomes ##EQU18##
The calculation of the intensity proceeds by taking an ensemble
average of .nu..nu.* with the grating orders producing multiple
illumination angles for the diffuser 18.
The expected intensity, normalized as in Equation (9), is
##EQU19##
The function F.sub.2 is the second order characteristic function of
the height h defined for a Gaussian distribution by
where r is the surface correlation function which is assumed to
depend on the separation of the points (x', y') and (x", y"). The
double summation can be broken into two summations in which j=l and
j.noteq.l as follows: ##EQU20##
For each integration, the variable substitution u=x'-x" and
.nu.=y'-y' is made, and the first integral is further simplified by
changing to polar coordinates since r.sub.12 is a function of
(u.sup.2 +.nu..sup.2) .sup.1/2. The evaluation of this first
integral is then identical to that in the description of the model
diffuser 26 (FIG. 2). In the second integral, s=x'+x" and w=y'+y"
to provide the following integral, ##EQU21##
The limits of s and w are on the order of the aperture and thus the
s integral, for an aperture substantially larger than the grating
spacing .LAMBDA., tends to zero due to the rapidly oscillating
exponential term. In Equation (26), just the first set of integrals
are left where j=l.
The intensity is evaluated to the following expressions for the
parabolic and conical correlation functions, respectively:
##EQU22##
where the rms phase delay is given by ##EQU23##
This is seen as the superposition of the individual diffuser
patterns from Equation (14) and (15) at the prescribed diffraction
angles weighted by the strengths of the diffraction orders.
These are also the results for the cascade of FIG. 1B and FIG. 1C.
The only difference is in the strengths of the diffraction orders
for a given grating profile.
Based on the total power that radiates in the forward direction
from the diffuser 18 in system 10, the parabolic correlation is
selected to be optimized since it has a higher power for a given S.
Maximum power occurs for roughness l.sub.c /(.lambda.S).gtoreq.1.
The width of the scattering lobe of the diffuser 18 decreases as
this parameter increases, i.e., as the diffuser becomes smoother.
The goal is to match a diffuser with a grating such that the first
diffraction order of the grating falls near the point at which the
lobe (i.e., power spectrum of the diffuser) is approximately
one-half (1/2) its peak value. This defines the grating spacing
.LAMBDA. in terms of l.sub.c /(.lambda.S).
The strengths of the diffraction orders required to obtain
uniformity of the intensity pattern over a large angular range (for
example, .+-.45.degree.) are described below for a single
wavelength. A parabolic diffuser with l.sub.c /(.lambda.S)=1 has a
full lobe width (to the 1/e point) of approximately 40.degree..
Therefore, a grating with a 20.degree. diffraction angle is chosen
at the desired wavelength. Such a grating will have 5 diffraction
orders: 0.degree., .+-.20.degree., and .+-.43.2.degree.. In FIG.
4A, the individual scattering patterns from the diffuser at these
incident angles and their sum are shown. The sum is the pattern
expected if all the grating diffraction orders were of equal
strength. Note that the peaks of the curves are shifted toward zero
degrees due to the cosine factor in the expected intensity. It is
at the peaks that the sum of all five individual scattering
patterns is optimized by choosing appropriate coefficients which
determine the strengths of the diffraction orders of grating 14.
Due to the symmetry of the patterns, only three coefficients are
needed since the + and - orders will be the same. The zero-order
coefficient, B.sub.0.sup.2 is set to 1 so that the other orders
will be scaled relative to it. Equation (28) can be written in the
simplified form of ##EQU24##
where I.sub.j is the individual intensity pattern for the j.sup.th
diffraction order and .theta..sub.m is the angular position of the
peak. At each .theta..sub.m, the sum is required to be a constant,
designated as C. Equation (31) is then rearranged and forms the
following matrix equation:
where the variables are ##EQU25##
Determining the unknown coefficients and the resulting sum is
provided by solving for B. Table I below lists the angles of the
peaks of the diffuser patterns for the 20.degree. grating, the
coefficients or relative strengths of the diffraction orders for a
uniform power distribution, and the final sum at the peak angles.
The coefficients are normalized by their total sum to conserve the
incident power. These values are also shown in Table I.
TABLE I Diffraction Order Peak Angle Coefficient, B.sup.2 j
Normalized by .SIGMA. B.sup.2.sub.j 0 0.0.degree. 1.0 0.141 .+-.1
.+-.18.80.degree. 0.588 0.083 .+-.2 .+-.37.70.degree. 2.450 0.346
Sum C 4.766 0.674
In FIG. 4B, the individual scaled diffuser patterns are shown using
the normalized coefficients along with their optimized sum for the
parabolic surface correlation. The optimized sum of the patterns is
fairly flat over a .+-.40.degree. angular spread with less than 10%
variation from the designed sum value within this angular range. To
decrease this variation, and further flatten the pattern requires
more closely-spaced diffraction orders and a narrower diffuser
pattern.
A parabolic diffuser with l.sub.c /(.lambda.S)=4 has a 1/e point of
about 5.degree.. A grating whose first diffraction order falls at
5.degree. will have 23 total orders with 17 in the range of
.+-.45.degree.. Although all 23 orders can be optimized, the higher
orders have large angular separations and will not yield satisfying
results. Therefore, the first 17 (from -8 to +8) are optimized with
the remaining six being scaled arbitrarily to the same coefficient
as the 8th order. FIG. 5A is a graph of the l.sub.c /(.lambda.S)=4
diffuser patterns at the diffraction angles of the 5.degree.
grating showing all 23 orders. There are nine unknown
quantities--eight coefficients for orders 1 to 8, and the resulting
sum. Again, the zero-order coefficient is set to 1. The optimizing
coefficients and their normalized values for a uniform power
distribution are shown in Table II below along with the peak angle
location of the diffuser patterns for the 5.degree. grating and the
final sum. The scaled diffuser patterns and the optimized result
are shown in FIG. 5B. The optimized intensity distribution is
substantially flat (i.e., uniform), varying less than 2% over the
.+-.45.degree. span (i.e., a wide angular range of 90.degree.).
TABLE II Diffraction Order Peak Angle Coefficient, B.sup.2 j
Normalized by .SIGMA. B.sup.2.sub.j 0 0.0.degree. 1.0 0.0318 .+-.1
.+-.4.98.degree. 1.006 0.0320 .+-.2 .+-.10.00.degree. 1.026 0.0327
.+-.3 .+-.15.10.degree. 1.059 0.0337 .+-.4 +20.32.degree. 1.111
0.0354 .+-.5 .+-.25.71.degree. 1.178 0.0375 .+-.6 .+-.31.34.degree.
1.302 0.0414 .+-.7 .+-.37.30.degree. 1.378 0.0439 .+-.8
.+-.43.71.degree. 1.786 0.0569 .+-.9 to .+-.11 1.786 0.0569 Sum C
81.698 2.601
To use optical system 10 (FIGS. 1A-C) as a part of a display
system, such as for a projection TV, an understanding of the
variation of these results with wavelength is important. Ideally,
the optimized intensity distribution from the diffuser-grating
cascade should be uniform over a broad spectrum. However, the
angular spread of the grating diffraction orders will change with
wavelength as given by the grating equation. With longer
wavelengths, the angular separation will increase, and the
intensity distribution from the cascade will tend to round over. At
shorter wavelengths, the diffraction angles will decrease and the
intensity distribution may tend to increase near the edges of the
optimization range.
If it is assumed that the grating transmission is due to a periodic
phase modulation arising from either an index variation, as in a
volume holographic grating, or a periodic height variation, as in a
surface relief grating, then the transmission function takes the
form
where L(x') is the periodic optical path length difference of the
transmitted wavefront. From Equation (16), another form for t.sub.G
is obtained, namely, ##EQU26##
Equating the phase of these expressions yields ##EQU27##
By changing the wavelength from .lambda..sub.0 to .lambda.' (or
wavenumber from k.sub.0 to k') the phase is changed from
.phi..sub.0 to ##EQU28##
Given the optimized coefficients of Table II at the designed
wavelength of 0.55 .mu.m, for example, the transmission function is
formed as in Equation (35). Phase is determined and scaled
according to Equation (37). This is then inserted into Equation
(34) from which a Fourier series is generated and the new
coefficients are determined.
There is an ambiguity in the sign of the original B.sub.j since the
optimization gives B.sub.j.sup.2. This ambiguity allows us the
flexibility to choose the sign of the coefficients that generates
the best diffuser pattern at a new wavelength. Table III below
lists the coefficients at three wavelengths: 0.45 .mu.m, 0.55
.mu.m, the optimized wavelength, and 0.65 .mu.m for the best result
for all possible sign permutations. The minus sign (-) indicates
which coefficients B.sub.j at the optimized wavelength were given a
negative value.
TABLE III Diffraction Order B.sub.j.sup.2 at 0.45 .mu.m
B.sub.j.sup.2 at 0.55 .mu.m B.sub.j.sup.2 at 0.65 .mu.m 0 0.0007375
0.0318 0.09963 1 0.07778 0.0320 0.01385 2 0.02465 0.0327 (-)
0.03487 3 0.03393 0.0337 (-) 0.03097 4 0.02988 0.0354 0.03537 5
0.03426 0.0375 0.03607 6 0.03800 0.0414 (-) 0.03855 7 0.03632
0.0439 (-) 0.04425 8 0.05548 0.0569 0.04943 9 0.05569 0.0569
0.05117 10 0.06731 0.0569 11 0.02717 0.0569 12 0.0005190 13
1.411E-6 14 9.344E-5
FIG. 6 shows the resulting grating-diffuser scattering patterns at
these three wavelengths, in which a significant variation from
uniformity in the patterns is shown, particularly near zero
degrees. It is observed that the zero-order coefficient from such
an analysis varies monotonically over this wavelength range for all
sign permutations. The optimized coefficient falls near the center
and the other two wavelengths give relatively high or low
coefficient values. The coefficients may be optimized at an extreme
wavelength, 0.45 .mu.m, for example, to provide calculated
coefficients at the other wavelengths which could produce better
results. The ideal values for the coefficients are shown in Table
IV for the three wavelengths.
TABLE IV Diffraction Order B.sub.j.sup.2 at 0.45 .mu.m
B.sub.j.sup.2 at 0.55 .mu.m B.sub.j.sup.2 at 0.65 .mu.m 0 0.0260
0.0318 0.0411 1 0.0262 0.0320 0.0415 2 0.0265 0.0327 0.0426 3
0.0271 0.0337 0.0446 4 0.0278 0.0354 0.0480 5 0.0292 0.0375 0.0519
6 0.0303 0.0414 0.0627 7 0.0334 0.0439 0.0627 8 0.0337 0.0569
0.0627 9 0.0421 0.0569 0.0627 10 0.0421 0.0569 11 0.0421 0.0569 12
0.0421 13 0.0421 14 0.0421
As shown by the above discussion, system 10 enables a uniform
intensity distribution over a wide angle from a cascade of a thin
surface diffuser 18 and an appropriately matched transmission
diffraction grating 14. The diffraction grating is thick relative
to the thin diffuser. The expected intensity pattern for the
cascade is given in Equation (28) and represents a linear
combination of the individual diffuser patterns when illuminated at
the grating diffraction orders. Uniformity is achieved by selecting
a grating diffraction angle equal to the one-half power point of
the diffuser and optimizing the strengths of the diffraction
orders. Thus, the angular intensity distribution of the diffraction
orders of the grating 14 when correlated with the power spectrum of
the diffuser 18 provides diffused light, which is substantially
uniform in intensity over an observation zone or plane within an
angular range. When the cascade is illuminated at wavelengths other
than the optimized wavelength(s), there may be a significant
departure from uniformity.
The result for the crossed grating configuration of system 10a of
FIG. 14A is similar to the result found for the single grating in
Equations (28) for the parabolic diffuser surface correlation, and
is given by ##EQU29##
The rms phase delay is ##EQU30##
To obtain a uniform circular symmetric intensity distribution, we
optimize the coefficients B.sub.j.sup.2 and B.sub.m.sup.2 over a
specified angular range .theta. and for all values of .phi..
FIG. 15A shows the optimization over a 90.degree. angular extent.
The result of Equation (38) has the added benefit of allowing us to
tailor the region of uniformity. For example, as shown in FIG. 15B,
we have produced an intensity distribution that is uniform over a
90.degree. horizontal range and a 30.degree. vertical range. Such a
result is ideal for a projection screen TV or the like. Other
tailored intensity distributions are also possible, as well as
asymmetric intensity distributions.
The result for the circular grating configuration of system 10a of
FIG. 14B for the parabolic diffuser surface correlation is
##EQU31##
where I.sub.0 is the modified Bessel function of the first kind,
order zero, and the rms phase delay, S, is given by Equation (30).
This result is always symmetric about the z axis since it is
independent of the polar angle .phi.. This result has been
optimized for a 90.degree. uniform circular symmetric pattern shown
in FIG. 15C. The result of the circular grating array in system 10b
of FIGS. 16A and 16B for a parabolic diffuser surface is
essentially the same as the above described result for a circular
grating. Furthermore, an elliptical grating, such as in an
elliptical grating array, may also be used having a similar result
to that of the circular grating, but providing an asymmetric
intensity pattern.
EXAMPLE 1
In optical system 10, a photoresist-coated substrate may provide
the grating 14 and etched glass as the diffuser 18 in this example.
The technique for producing gratings is well known. The gratings
were produced by spin coating a 5 cm.times.5 cm cover glass
substrate with Shipley S1827 photoresist at 4000 rpm. This gives a
2.7 .mu.m thick resist layer. The resist was soft baked at
95.degree. C. for 30 min. and given an initial blanket exposure of
24 mJ/cm.sup.2 of ultraviolet light. The resist was exposed to a
sinusoidal fringe pattern created by the interference of two 4.5 cm
diameter beams of the 457 nm line of a single frequency argon
laser. The average exposure energy was 675 mJ/cm.sup.2 for a fringe
peak of 1.35 J/cm.sup.2. This high exposure energy is required
because of the decreased sensitivity of the photoresist at this
wavelength and the large thickness of the resist. The beam angle
determines the fringe spacing and the resulting grating spacing
formed in the photoresist. After exposure, the resist was developed
by spraying with Shipley 452 Developer for 6 seconds and rinsed
with de-ionized water as the substrate was spun at 1000 rpm. The
length of the exposure and of the development time determine the
depth of the surface relief in the photoresist. For short
development times the resist takes on a sinusoidal relief profile.
As the development time increases, the profile becomes less
sinusoidal and eventually attains a scalloped shape. The developer
etches in a direction perpendicular to the local
photoresist-solution interface, thus the peaks become sharper and
the valleys become broader. Eventually, the pattern submerges into
the resist unchanged. By controlling the length of the exposure and
development the shape and depth of the profile is controlled and
subsequently the strengths of the diffraction orders. A 5.degree.
grating was fabricated with the resulting diffraction order
strengths in Table V, as a fraction of incident power, at three
wavelengths of 0.457 .mu.m, 0.514 .mu.m and 0.632 .mu.m for the
orientation of FIG. 1A. It shows strong orders up to
.+-.30.degree..
TABLE V Diffraction Order 0.457 .mu.m 0.514 .mu.m 0.632 .mu.m 0
0.0937 0.129 0.0828 1 0.0351 0.0037 0.0741 2 0.0374 0.0877 0.158 3
0.0930 0.104 0.0822 4 0.0679 0.0540 0.283 5 0.0318 0.0204 0.0088 6
0.0126 0.0071 0.0037 7 0.0046 0.0029 0.0030 8 0.0020 0.0019 0.0057
9 0.0013 0.0013 10 0.0001 0.0023 11 0.0013
The total power throughput of the grating in this example was
measured using a 10 inch diameter integrating sphere with the
grating placed at a 1/4 inch diameter entrance pupil. The grating
was separately illuminated with a small diameter laser beam at each
of the above three wavelengths. A 1 cm.sup.2 photodetector was
positioned at a 1/2 inch diameter exit pupil at 90.degree. to the
illumination and above the plane of the diffraction orders. The
detected power from the grating was measured relative to the
incident illumination with a beam power measurement.
For the beam power measurement the unobstructed laser beam entered
the integrating sphere and a power reading was taken at an off-axis
port. A baffle was positioned to prevent any first strike
reflections from hitting the detector. Power throughout
measurements of the grating of 74% at 0.457 .mu.m, 78% at 0.514
.mu.m, and 88% at 0.632 .mu.m were obtained. The photoresist is a
blue absorbing material hence the decreased transmission in the
blue.
ZYGO Nu View white light profilometer with a lateral resolution of
1.1 .mu.m was used to profile the grating. The instrument works by
forming white light fringes on the image of a surface and tracking
the position of the fringes as the surface is translated
vertically. The grating was determined to have a period of 5.25
.mu.m and a height variation of 0.8 .mu.m. The precise shape of the
profile was assumed to be sinusoidal. For purposes of illustration,
a scanning electron micrograph of a grating suitable for use in
this example is shown in FIG. 7 and does present a sinusoidal
profile. The height variation of this grating is determined to be
approximately 0.76 .mu.m.
The diffuser in this example is made from a 2".times.2" cover glass
exposed on one side in varying durations to different etchants.
Armour Etch etching cream is used on the smooth, cleaned surface to
preroughen the surface. The surface characteristics are critically
dependent on the initial duration of the exposure and change
significantly during the first few minutes. At an etching time with
the cream of approximately 45 min., the texture of the surface does
not appear to change. The preroughing produces a conical surface
correlation as described earlier. The surface is then exposed to
BOE (Basic Oxide Etch). Once preroughened with the cream, the BOE
has the effect of smoothing out the high frequency detail of the
surface. The surface is exposed to the BOE for up to 2 hours. With
a 60 min. exposure to the Armour Etch, a 2 min. exposure of BOE
gives an l.sub.c /(.lambda.S) value of 3, 5 min. of BOE gives
l.sub.c /(.lambda.S)=3.2, 20 min. gives l.sub.c /(.lambda.S)=4, 50
min. gives l.sub.c /(.lambda.S)=5.8, and 120 min. of BOE exposure
gives l.sub.c /(.lambda.S)=12.8.
The diffuser has a scattering pattern that can be characterized at
small angles by Equation (14) for the parabolic surface
correlation. The total power throughput using the integrating
sphere is 95%. For this measurement the baffle in the integrating
sphere was positioned to prevent direct scattered light from the
diffuser from hitting the detector.
The system used for the scattering pattern measurements consists of
a silicon PIN photodiode operating in the photovoltaic mode mounted
on an arm that swings in an arc centered at the diffuser. The
incident laser illumination is polarized perpendicular to the plane
of the arc and the detector contains a similarly oriented analyzer.
The detector subtends an angle of 0.22.degree. and is stepped in
0.2.degree. increments through computer control. The laser beam
from an argon ion laser is modulated with a chopper at 930 Hz and
the detected signal is fed through a preamplifier and into a
lock-in amplifier to provide intensity measurements over 10 orders
of magnitude. The measured voltage is normalized by a reference
voltage taken from a second detector in the input beam to monitor
beam fluctuations. The single beam scattering pattern of the
diffuser for normal incidence is shown in FIG. 8 for a wavelength
of 0.514 .mu.m. The relative intensity is plotted on a logarithmic
scale and has a half-power lobe width of 11.6.degree.. The amount
of scattering at wider angles indicates that the surface also has a
conical correlation component, but it is small. The roughness
parameter, l.sub.c /(.lambda.s), is found to be 2.6. For comparison
to the incident power level, an undisturbed laser beam signal for
this system is 2300. This applies to all the data plots.
The 5.degree. grating and the diffuser of this example were
cascaded as in FIG. 1A and the radiation pattern in the plane of
the diffraction orders was measured. The result in FIG. 9 shows
substantial uniformity over a 40.degree. span and at all three
wavelengths. The power throughput for the cascade ranges from 67%
at 0.457 .mu.m and 0.514 .mu.m to 77% at 0.632 .mu.m. This can be
compared to a commercially available microfiche viewer screen shown
in FIG. 10 which has a symmetric distribution and a total power
throughput of about 55% for blue and green and 45% for red. The
screen is in fact blue accounting for the reduced transmission in
red.
EXAMPLE 2
The optimum diffraction orders provided by the diffraction grating
14 in system 10 may be provided by more than one diffractive
element, such as shown for example in the system 28 of FIG. 11A.
Multiple diffraction gratings can be used to provide additional
diffraction orders to the diffuser or when it is difficult to
fabricate a single grating having the desired number of orders at
the desired multiple wavelengths, such as more than 5 or 6 optimum
orders at three wavelengths. System 28 operates the same as system
10 except that two diffraction gratings 14a and 14b are used with
diffuser 18, instead of a single diffraction grating. Diffraction
gratings 14a and 14b may be on different optical elements or two
surfaces of the same optical element. In this example, a second
grating 14b with a 15.degree. diffraction angle is added to the
system of the previous example, where grating 14a is a 5.degree.
grating oriented as the grating shown in FIG. 1A, and grating 14b
and diffuser are oriented as shown in FIG. 1B. The second grating
14b effectively replicates the orders of the 5.degree. grating 14a
at the larger angles. FIG. 11B shows the scattering pattern
produced by system 28 having a substantially flat (i.e., uniform)
pattern over an 80.degree. range at all three wavelengths.
Thus, as shown by these examples, the systems 10 and 28 can provide
for the diffusing of light with a uniform intensity pattern and no
color effects, such as color banding. In particular, a cascade of
grating 14 and diffuser 18 having the performance illustrated in
FIGS. 9 and 11B (i.e., a uniform intensity distribution over a wide
angular range of 80.degree. at multiple wavelengths) is applicable
to a projection TV screen, display screen (such as a computer CRT
or LCD), or the like, or for general purpose illumination.
Controlled lighting situations other than uniform are also possible
by altering the strengths of the grating diffraction orders as
desired. The above examples are illustrative of the optical system
for diffusing light shown in FIGS. 1A, 1B, and 1C, and FIG. 11A.
Other combinations of diffractive and diffusing elements having the
desired optimum diffractive orders and diffusing characteristics
may also be used.
From the foregoing description, it will be apparent that there has
been provided an improved optical system for diffusing light.
Variations and modifications in the herein described system in
accordance with the invention will undoubtedly suggest themselves
to those skilled in the art. For example, the optical system may be
used for diffusing electromagnetic signals other than visible
light, such as in the spectrum of radio signals through microwave,
sub-mm, infrared, ultraviolet and x-ray, by optimizing the system
for wavelengths or wavelengths of such signals. Accordingly, the
foregoing description should be taken as illustrative and not in a
limiting sense.
* * * * *